limn→∞(1n2+1+2n2+1+3n2+1+…+2nn2+1)=______.-数学

题目简介

limn→∞(1n2+1+2n2+1+3n2+1+…+2nn2+1)=______.-数学

题目详情

lim
n→∞
(
1
n2+1
+
2
n2+1
+
3
n2+1
+…+
2n
n2+1
)
=______.
题型:填空题难度:中档来源:卢湾区一模

答案

设A=class="stub"1
n2+1
+class="stub"2
n2+1
+class="stub"3
n2+1
+…+class="stub"2n
n2+1
=class="stub"1+2+3+…+2n
n2+1
=
2n2+n
n2+1

所以
lim
n→∞
(class="stub"1
n2+1
+class="stub"2
n2+1
+class="stub"3
n2+1
+…+class="stub"2n
n2+1
)
=
lim
n→∞
A=
lim
n→∞
2n2+n
n2+1
=2

故答案为2.

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